Free falling objects and the equations to calculate velocity and distance A The acceleration due to gravity is on average 9 81 m s2 1 Round to 10 m s2 in classroom discussions examples homework 2 The more precise number is used in lab 3 Variables in equations a a is used to represent acceleration in equations b g is used in equations to represent the acceleration of gravity acting on falling objects B How fast is the object going after a certain amount of time that if falls 1 gains speed for each second it falls 10 m s for each second 2 calculate how fast by the equation v gt 3 this is its instantaneous velocity not its average velocity 4 objects tossed upward slow down at this acceleration too II Projectile motion A involves objects moving along curved paths 1 horizontal movement are constant velocity motions 2 vertical movements are accelerated motions 3 independent of one another B object projected by some means that continues in motion under influence of gravity Separate investigation of horizontal and vertical motion 1 horizontal neglecting friction a no change in velocity b equal distances in equal times c no acceleration 2 vertical like freely falling objects a accelerate due to gravity b velocity changes c falls farther during each successive time interval 3 each component act independently of one another C ball rolling forward and continues off the tabletop 1 see ball from top a horizontal movement b not affected by vertical l movement c does not affect vertical movement 2 see ball from front a vertical movement b not affected by horizontal movement c does not affect horizontal movement D projectile moving upward initially in addition to forward 1 without gravity or friction a it would continue upward diagonally b we will ignore friction 2 gravity acts vertically independent of horizontal velocity a falling from the no gravity path b just as far as if it had been dropped from the no gravity path at the instant it was launched upward in the gravity environment I 3 III IV V VI no acceleration in horizontal direction after it is fired a moves equal distance forward for each time interval b there is no forward acceleration only speed 4 the vectors of horizontal and vertical velocity represent these Projectile examples A Cannonball 1 without gravity 2 gravity is external force a horizontal acceleration is zero no change in speed b vertical acceleration is 10m s2 B airplane and package problem 1 40 m s forward velocity of plane and package 2 falls to directly below the plane C cannonball shot at angle 1 path diagonal without gravity 2 path parabola with gravity D Monkey and zookeeper animations 1 Without gravity straight to him 2 With gravity fast shot 3 With gravity slower shot E calculate how fast cannon ball is going in vertical and horizontal direction 1 horizontal speed constant 2 vertical speed varies with time 3 overall speed calculated with vectors of each added together Projectile Range A Steepness affects how long it is in the air 1 complementary angles have same range 2 greatest range at 45o angle B vertical speed is zero at top of trajectory C consider air resistance Calculations of speed A Baseball from 5 m platform 1 know height and distance of throw 2 know vertical d 1 2 gt2 g and d 3 find t to fall 4 divide horizontal distance by t B Curvature of Earth 5 m vertical for each 8000 m horizontal 1 if you could throw 8000 m s ball would never reach the ground 2 same principle for orbiting objects Rotational speed A Directly proportional to distance from center of rotation B Cones roll in circles 1 smaller diameter goes slower less distance in one rotation 2 greater diameter goes faster further in one rotation 3 this is why train wheels are made like they are
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